Question

The students present in an auditorium are asked to stand in rows. If there were 4 students extra in a row there would be 4 less rows. However, if 2 students were less in a row, there would be 4 more rows. The number of students present in the auditorium is

• A. 80
• B. 96
• C. 100
• D. 128

Answer 1

The Correct Option is B

Let there are r rows and \(x\) students in each row 
According to question
(\(x\)\(+\)4)(r−4) = \(x\)×r
\(⇒\) −4\(x\)\(+\)4r = 16    ………..(i)
(\(x\)−2) \(\times\)(r\(+\)4) = \(x\)×r
4\(x\)−2r = 8            …………..(ii)
Adding equations (i) and (ii), we get 
2r = 24
r = 12
4\(x\)−24 = 8
\(x\)=8.
Total number of students = 8×12 = 96.
So, the correct option is (B)